“How Many: A Counting Book” by Christopher Danielson is a very simple yet brilliantly composed book of pictures about counting. There are no right answers, and Danielson states at the start of the book:

“This is a book about numbers and counting, but it’s different from other counting books. This book doesn’t tell you what to count. It doesn’t start with small numbers and end with big ones.”

In each picture, or set of pictures, there are choices as to what the reader will count. A pair of shoes in a box might lead a reader to say there is one pair of shoes, while another reader might say there are two shoes. Yet another reader might say there is one box of shoes, and yet others might count the shoelaces or the holes for the shoelaces.

An example of great math thinking happened when I showed this book to a group of kindergarteners. While looking at the first page, Jean said that she would probably count the holes for the shoelaces on the pair of shoes. I asked her how many, and she counted five holes on one side, she told us she assumed all the holes would be in groups of five, and she said, “There are 20 holes.” I asked how she knew there were 20, and she said that “five, four times is 20.” Another student, Julian, said, “If you put 5 and 5 together, it makes 10, and if you put another 5 and 5 together, it makes 10. Then you add 10 and 10 and get 20.” Perfect mathematical thinking! Expressed in words and in action.

Miranda then commented that although it looks like there are 4 shoelaces, there are really only two. About half the students thought there were two shoelaces on each shoe while the others thought that each shoe had only one shoelace. We tried to find a student wearing shoes with real shoelaces, but all the laces were the pretend elastic kind! We did talk about shoelaces, though.

Kids will think it’s a game and love that there are myriad right answers. And the longer they stare at the pictures, the more numbers they might come up with. For teachers, there is a teacher’s guide. (Parents and educators will find the guide filled with important information about mathematical thinking and the book.) The teacher’s guide is not just a simple “how to” guide for the picture book. Rather, it’s a 100-page guide to children’s mathematical thinking and understanding. Sure, it gives fabulous ideas about how to use the book, but it’s much, much more.

Every math teacher and every parent should read it. They will see the world around them differently and enable their students to do so as well.

Please note: This review is based on the final books provided by the publisher, Stenhouse Publishers, for review purposes.